**The professional title obtained is Doctor of Mathematical Sciences or Doctor of Computer Science/Science**

Curriculum for the 3rd cycle of study “Mathematical Sciences in Southeast Europe” (valid for students enrolled from the academic year 2021/22)

(Curriculums and programs that were valid for students enrolled until the academic year 2020/2021)

Code | Course Title | No. contact hours | ECTS |
---|---|---|---|

EDU 610 | Methodology of Research and Academical Skills | 30 | 10 |

Elective Course 1 | 30 | 10 | |

Elective Course 2 | 30 | 10 |

Code | Course Title | No. contact hours | ECTS |
---|---|---|---|

Elective Course 3 | 30 | 10 | |

Elective Course 4 | 30 | 10 | |

Elective Course 5 | 30 | 10 |

Code | Course Title | No. contact hours | ECTS |
---|---|---|---|

Work on Doctoral Thesis-Doctorial Seminar | 30 |

Code | Course Title | No. contact hours | ECTS |
---|---|---|---|

Work on Doctoral Thesis | 30 |

Code | Course Title | No. contact hours | ECTS |
---|---|---|---|

Work on Doctoral Thesis | 30 |

Code | Course Title | No. contact hours | ECTS |
---|---|---|---|

Defense of Doctoral Thesis | 30 |

Courses that have an exclusively optional status

It is necessary to choose two subjects from those suggested below:

Code | Course Title |
---|---|

PMAT 605 | Algorithmic Number Theory |

AMAT 605 | Topological Dynamical Systems |

PMAT 610 | Abstract Algebra and Graphs |

AMAT 610 | Constrained and Unconstrained Optimization |

CS 605 | Algorithms and Data Structures II |

AMAT 615 | Dynamical Systems |

PMAT 615 | Finite Fields and Their Applications |

PMAT 620 | Theory of Harmonic Functions |

PMAT 625 | General Functions |

CS 610 | Intelligent Systems |

PMAT 630 | Algebraic Topology I |

PMAT 635 | Integral Operators |

PMAT 640 | Generalized Functions and Transformations |

PMAT 645 | Algebraic Number Theory |

AMAT 625 | Numerical Methods for Solving Linear and Nonlinear Eigenvalues Problems |

AMAT 620 | Monotone Dynamic Systems |

PMAT 650 | Combinatorics |

Courses that have an exclusively optional status

It is necessary to choose three subjects from those suggested below:

Code | Course Title |
---|---|

AMAT 655 | Continuous Dynamical Systems |

AMAT 660 | Parameter Estimation |

AMAT 665 | Numerical Simulations |

CS 655 | Calculations of High Performance |

PMAT 655 | Algebraic Combinatorics |

PMAT 660 | Harmonic Analysis |

PMAT 665 | Spectral Theory of Automorphic Forms |

PMAT 670 | Spectral Graph Theory |

PMAT 675 | AAnalysis on Manifolds |

AMAT 670 | Selected Topics in Cryptography |

PMAT 680 | Noncommucative Rings |

PMAT 685 | Analytic Number Theory II |

AMAT 675 | Chaos |

AMAT 680 | Stochastic Processes II |

CS 660 | Theory of Complexity |

AMAT 685 | Numerical Methods for Large Nonlinear Systems |

PMAT 690 | Algebraic Topology II |

PMAT 695 | Cayley Graphs of Semigroups |

## Rules of study in the 3rd cycle of studies

In the 1st semester, all candidates are required to take the subject “Research Methodology and Academic Skills” and two subjects from the offered list of subjects for the 1st semester, which will be determined for each candidate by the VDS of the Department of Mathematics, in accordance with the candidate’s research interests. In the second semester, the candidate takes three subjects from the offered list of subjects for the second semester, which will be determined for each candidate by the VDS of the Department of Mathematics, in accordance with the candidate’s research interests. In the 3rd semester, the candidate is obliged to defend a “Doctoral Seminar” with a supervisor/potential mentor that carries 30 ECTS and is related to work on a doctoral dissertation, which is called “Work on a doctoral dissertation – Doctoral Seminar”. Doctoral seminars are not evaluated, but its successful defense is verified in the index.

In the IV and V semesters, the candidate works on the working version of the doctoral dissertation, which is called “Doctoral dissertation work”, which is verified by the mentor in the index with his signature, and which carries 30 ECTS per semester, without a grade.

In the 6th semester, the candidate is entitled to 30 ECTS for the preparation and defense of the doctoral dissertation, which is verified by the mentor with his signature.

A candidate can take a maximum of two courses with one teacher during his doctoral studies.

The candidate acquires one of the titles provided by the Law, in accordance with the field to which the topic of his doctoral dissertation belongs